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Chirality

Chirality

Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...

Chirality in Nature

Chirality in Nature

Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid.

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality is most prevalent in carbon-based tetrahedral compounds, but this important facet of molecular symmetry extends to sp3-hybridized nitrogen, phosphorus and sulfur centers, including trivalent molecules with lone pairs. Here, the lone pair behaves as a functional group in addition to the other three substituents to form an analogous tetrahedral center that can be chiral.
A consequence of chirality is the need for enantiomeric resolution. While this is theoretically possible for all...

Molecules with Multiple Chiral Centers

Molecules with Multiple Chiral Centers

Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...

Fischer Projections

Fischer Projections

Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines.

Prochirality

Prochirality

The concept of prochirality leads to the nomenclature of the individual faces of a molecule and plays a crucial role in the enantioselective reaction. It is a concept where two or more achiral molecules react to produce chiral products. A typical process is the reaction of an achiral ketone to generate a chiral alcohol. Here, the achiral reactant reacts with an achiral reducing agent, sodium borohydride, to generate an equimolar mixture of the chiral enantiomers of the product. For example, an...

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Related Experiment Video

Updated: Jun 5, 2025

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

Spinless topological chirality from Umklapp scattering in twisted 3D structures.

Cong Chen¹, Xu-Tao Zeng², Wang Yao¹

¹Department of Physics, The University of Hong Kong, The University of Hong Kong, Pokfulam, Hong Kong, Hong Kong, 999077, HONG KONG.

Reports on Progress in Physics. Physical Society (Great Britain)

|December 13, 2024

Summary

Researchers discovered novel spinless topological chiralities arising from structural patterns in twisted graphite. This opens new avenues for designing topological materials for photonics and acoustics.

Keywords:

Z2 gauge field higher-order Dirac semimetal intervalley Umklapp scattering spinless chiral Weyl semimetal topological chirality

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Area of Science:

Condensed Matter Physics
Materials Science
Topological Materials

Background:

Spinless systems possess unique topological properties distinct from spinful counterparts.
The interplay between topological and structural chirality in spinless systems remains largely unexplored.

Purpose of the Study:

To discover and characterize spinless topological chiralities originating purely from structural chirality.
To explore novel topological phases in 3D patterned, structureless materials.

Main Methods:

Theoretical investigation of twisted graphite systems with specific 3D spatial patterning.
Analysis of bulk topology and surface/hinge states using concepts like intervalley Umklapp scattering.
Introduction of a $\pi$-flux $\mathbb{Z}_2$ lattice gauge field to explain altered symmetry algebra.

Main Results:

Discovery of a chiral Weyl semimetal phase in a 3D screw twisted structure, with topology dictated by the screw direction.
Identification of a higher-order Dirac semimetal with chiral hinge states in a 3D periodic structure with alternating twist angles.
Unveiling intervalley Umklapp scattering as the mechanism capturing interface chirality and inducing effective chiral interlayer hopping.

Conclusions:

Spinless topological chiralities can be engineered solely through the 3D structural patterning of featureless units.
This work establishes a new paradigm for designing topological materials by manipulating structural chirality.
Findings have implications for advancing topological photonics and acoustics.